We report direct measurements of the valley susceptibility, the change of valley population in response to applied symmetry-breaking strain, in an AlAs two-dimensional electron system. As the two-dimensional density is reduced, the valley susceptibility dramatically increases relative to its band value, reflecting the system's strong electron-electron interaction. The increase has a remarkable resemblance to the enhancement of the spin susceptibility and establishes the analogy between the spin and valley degrees of freedom.PACS numbers: 71.70.Fk , 73.43.Qt Currently, there is considerable interest in controlled manipulation of electron spin in semiconductors. This interest partly stems from the technological potential of spintronics, namely, the use of carrier spin to realize novel electronic devices. More important, successful manipulation of spins could also impact the more exotic field of quantum computing since many of the current proposals envision spin as the quantum bit (qubit) of information [1,2,3]. Here we describe measurements of another property of electrons, namely their valley degree of freedom, in a semiconductor where they occupy multiple conduction band minima (valleys) [ Fig. 1(a)]. Specifically, for a two-valley, two-dimensional electron system (2DES) in an AlAs quantum well, we have determined the "valley susceptibility", χ v , i.e., how the valley populations respond to the application of symmetry-breaking strain. This is directly analogous to the spin susceptibility, χ s , which specifies how the spin populations respond to an applied magnetic field [Figs. 1(d)]. Our data show that χ v and χ s have strikingly similar behaviors, including an interaction-induced enhancement at low electron densities. The results establish the general analogy between the spin and valley degrees of freedom, implying the potential use of valleys in applications such as quantum computing. We also discuss the implications of our results for the controversial metal-insulator transition problem in 2D carrier systems.It is instructive to describe at the outset the expressions for the band values of spin and valley susceptibilities χ s,b and χ v,b [4]. The spin susceptibility is defined as χ s,b = d∆n/dB = g b µ B ρ/2, where ∆n is the net spin imbalance, B is the applied magnetic field, g b is the band Landé g-factor, and ρ is the density of states at the Fermi level. Inserting the expression ρ = m b /πh 2 for 2D electrons, we have χ s,b = (µ B /2πh 2 )g b m b , where m b is the band effective mass. In analogy to spin, we can define valley susceptibility as χ v,b = d∆n/dǫ = ρE 2,b = (1/πh 2 )m b E 2,b , where ∆n is the difference between the populations of the majority and minority valleys, ǫ is strain, and E 2,b is the conduction band deformation potential [5]. In a Fermi liquid picture, the interparticle interaction results in replacement of the parameters m b , g b , and E 2,b [6] by their normalized values m * , g * , and E * 2 . Note that χ s ∝ m * g * and χ v ∝ m * E * 2 . Our experiments were performed on...
Two-dimensional electrons in AlAs quantum wells occupy multiple conduction-band minima at the Xpoints of the Brillouin zone. These valleys have large effective mass and g-factor compared to the standard GaAs electrons, and are also highly anisotropic. With proper choice of well width and by applying symmetry-breaking strain in the plane, one can control the occupation of different valleys thus rendering a system with tuneable effective mass, g-factor, Fermi contour anisotropy, and valley degeneracy. Here we review some of the rich physics that this system has allowed us to explore.
Using a novel technique, we make quantitative measurements of the spin polarization of dilute [ (3.4-6.8)x10(10) cm(-2)] GaAs (311)A two-dimensional holes as a function of an in-plane magnetic field. As the field is increased the system gradually becomes spin polarized, with the degree of spin polarization depending on the orientation of the field relative to the crystal axes. Moreover, the behavior of the system turns from metallic to insulating before it is fully spin polarized. The minority-spin population at the transition is approximately 8x10(9) cm(-2), close to the density below which the system makes a transition to an insulating state in the absence of a magnetic field.
We report a manifestation of first-order magnetic transitions in two-dimensional electron systems. This phenomenon occurs in aluminum arsenide quantum wells with sufficiently low carrier densities and appears as a set of hysteretic spikes in the resistance of a sample placed in crossed parallel and perpendicular magnetic fields, each spike occurring at the transition between states with different partial magnetizations. Our experiments thus indicate that the presence of magnetic domains at the transition starkly increases dissipation, an effect also suspected in other ferromagnetic materials. Analysis of the positions of the transition spikes allows us to deduce the change in exchange-correlation energy across the magnetic transition, which in turn will help improve our understanding of metallic ferromagnetism.Ferromagnetism in metallic systems, also known as itinerant electron ferromagnetism, has thus far revealed few of its secrets to scientists. In one of its well-known occurrences, in transition elements Fe, Co, and Ni, metallic ferromagnetism is believed to stem from a partially filled 3d band of electrons with unbalanced spin populations, although the properties of their magnetic moments at nonzero temperature are still unclear (1) despite some recent theoretical progress (2). In dilute electron gases, the appearance of spontaneous magnetization at sufficiently low densities, as evidenced by recent experiments in doped hexaborides (3), is also subject to debate, with the critical density at the ferromagnetic to paramagnetic transition still uncertain (4). One difficulty in modeling these materials lies in their complexity, because itinerant charged carriers in these systems are subject not only to electron-electron interactions, but also to atomic potentials resulting in an intricate density of states or to local moments of other atoms in the material. Two-dimensional (2D) electron systems in modulationdoped semiconductor heterostructures, on the other hand, provide an ideal system for the study of itinerant electron ferromagnetism, as interactions with their host material are almost entirely contained in the effective mass (m * ) and effective g-factor (g * ) of electrons. Given these two renormalizations, carriers in these structures behave as a nearly free electron gas. In a perpendicular magnetic field (B ⊥ ), 2D electrons condense into a ladder of energy levels, called Landau levels, which are separated by the cyclotron energyhω c =heB ⊥ /m * . The total magnetic field (B tot ) also couples to the electron spin, and leads to an additional (Zeeman) energy ± 1 2 |g * |µ B B tot (where µ B is the Bohr magneton, eh/2m e , and m e is the bare electron mass), which splits each Landau level into two separate levels. The number of occupied spin-split Landau levels at a given field is called the filling factor, ν. This discrete level structure gives rise to the quantum Hall (QH) effect, the vanishing of longitudinal resistance (R xx ) and the quantization of the Hall resistance, that occurs when an integral nu...
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